👉 Expansion math, also known as expansion matrices or tensor product matrices, is a mathematical operation used to combine two or more matrices (or tensors) into a larger matrix. When you multiply a matrix A of size m x n by another matrix B of size p x q, the resulting matrix C will be of size m x q. Each element C[i][j] is computed as the dot product of the i-th row of A and the j-th column of B. This operation is fundamental in various fields such as linear algebra, quantum mechanics, and machine learning, enabling the representation of complex transformations and interactions between different mathematical structures. The expansion essentially captures how elements from one matrix can be combined with elements from another to form a new, larger structure, which is crucial for operations like tensor decompositions and multi-dimensional data analysis.
